Born in Ludwigshafen am Rhein, Zwißler studied at the music universities of Heidelberg and Munich from 1920 to 1924, and the following year at the Akademie der Künste in Berlin.
Three years later he went as conductor to the Deutsche Oper (German Opera) in Brno,[2][3] followed by Düsseldorf and Darmstadt.
[3][2] In these years, he conducted works by Igor Stravinsky, although the composer's works were regarded as Entartete Musik (degenerate music): the suite from Petrushka, the Symphony of Psalms, a production of the ballet The Firebird, and the German premiere of the concerto Dumbarton Oaks.
[2] From 1956, Zwißler taught at the Hochschule für Musik und Darstellende Kunst Stuttgart.
From 1958, he taught conducting at the Hochschule für Musik und Darstellende Kunst Frankfurt am Main, and was appointed professor a year later.